I briefly review our general knowledge of positron astrophysics, focusing mostly on the theoretical and modelling aspects. The experimental/observational aspects of the topic have recently been reviewed elsewhere [E. Churazov et al., Mon. Nat. R. Astron. Soc. 411, 1727 (2011); N. Prantazos et al., Rev. Mod. Phys. 83, 1001 (2011)]. In particular, I highlight the interactions and cross sections of the reactions that the positrons undergo in various cosmic media. Indeed, these must be of high interest to both the positron astrophysics community and the low-energy positron physics community in trying to find common areas of potential collaboration for the future or areas of research that will help the astrophysics community make further progress on the problem. The processes undergone by positrons from the moments of their birth to their annihilation (in the interstellar medium or other locations) are thus examined. The physics of the positron interactions with gases and solids (dust grains) and the physical conditions and characteristics of the environments where the processes of energy loss, positronium formation, and annihilation take place, are briefly reviewed. An explanation is given about how all the relevant physical information is taken into account in order to calculate annihilation rates and spectra of the 511 keV emission in the ISM; special attention is paid to positron interactions with dust and with polycyclic aromatic hydrocarbons. In particular, an attempt is made to show to what extent the interactions between positrons and interstellar dust grains are similar to laboratory experiments in which beams of low-energy positrons impinge upon solids and surfaces. Sample results are shown for the effect of dust grains on positron annihilation spectra in some phases of the ISM which, together with high resolution spectra measured by satellites, can be used to infer useful knowledge about the environment where the annihilation is predominantly taking place, and ultimately about the birth place and history of positrons in the Galaxy. The important complementarity between work done by the astrophysical and the positron physics communities is emphasised, and attempts are made to suggest avenues of future research for progress in the two fields.